一类金融衍生产品的二叉树方法

THE METHOD OF BINARY TREE ABOUT FINANCIAL DERIVATIVES

文章首先介绍了期权及外汇理财产品的性质特点和风险,然后说明了中国银行发行的外汇宝:“美元稳健进取”理财产品的具体条款．其次利用Δ-对冲思想和Ito公式建立了外汇理财产品的偏微分方程定价模型,利用偏微分方程的理论,给出了该模型的解的形式．并利用二叉树方法进行了数值计算,得到产品在t=0时的价值．然后我们对不同的波动率,美元利率,欧元利率进行分析,得到的结论是:产品的价值与波动率、美元利率、欧元利率呈反比．

We first introduce the financial product in the market and take a financial product issued by The Bank of China called ‘making money by dollars＇ as a sample of options in the current financial market of China. Then by using the △-hedging theory and Ito formula, we establish a partial differential equation model. By the theory of partial differential equation, we give the solution of the model. Then we use numerical method to compute the value of the product, especially at time t = 0. Finally we discuss the change of price of the product with several variables or parameters such as the riskless interest rate of Eurocurrency and the exchange rate between Dollars and Eurocurrency.